A first application of the kernel distance is in the visualization of kernel spaces and data in general [1]}, [2]}. The embedding method employed here is the so called mutidimensional scaling (MDS) one (see, e.g. [3]}).
More precisely, given \(N\)  points \(p_1,\ldots ,p_N\) , we can approximate their position in a kernel space \(\mathcal {H} \subset \mathbb {R}^d\)  by \(y_1,\ldots ,y_N \in \mathbb {R}^d\) , by minimizing the cost-function
\(J = \sum _{i = 1}^N\sum _{j > i}^N(||y_i - y_j|| - D_{ij})^2\,.\) 
